Template:Three-parameter weibull distribution: Difference between revisions

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The three-parameter Weibull ''pdf'' is given by:  
The 3-parameter Weibull ''pdf'' is given by:  


::<math> f(t)={ \frac{\beta }{\eta }}\left( {\frac{t-\gamma }{\eta }}\right) ^{\beta -1}e^{-\left( {\frac{t-\gamma }{\eta }}\right) ^{\beta }} </math>  
::<math> f(t)={ \frac{\beta }{\eta }}\left( {\frac{t-\gamma }{\eta }}\right) ^{\beta -1}e^{-\left( {\frac{t-\gamma }{\eta }}\right) ^{\beta }} \,\!</math>  


where:  
where:


::<math> f(t)\geq 0,\text{ }t\geq 0\text{ or }\gamma, </math>
::<math> f(t)\geq 0,\text{ }t\geq \gamma \,\!</math>


::<math>\beta>0\ \,\!</math>
::<math>\beta>0\ \,\!</math>
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::<math> \eta > 0 \,\!</math>
::<math> \eta > 0 \,\!</math>


::<math> -\infty < \gamma < +\infty \\!</math>
::<math> -\infty < \gamma < +\infty \,\!</math>


and:  
and:  

Latest revision as of 17:50, 6 July 2017

The 3-parameter Weibull pdf is given by:

[math]\displaystyle{ f(t)={ \frac{\beta }{\eta }}\left( {\frac{t-\gamma }{\eta }}\right) ^{\beta -1}e^{-\left( {\frac{t-\gamma }{\eta }}\right) ^{\beta }} \,\! }[/math]

where:

[math]\displaystyle{ f(t)\geq 0,\text{ }t\geq \gamma \,\! }[/math]
[math]\displaystyle{ \beta\gt 0\ \,\! }[/math]
[math]\displaystyle{ \eta \gt 0 \,\! }[/math]
[math]\displaystyle{ -\infty \lt \gamma \lt +\infty \,\! }[/math]

and:

[math]\displaystyle{ \eta= \,\! }[/math] scale parameter, or characteristic life
[math]\displaystyle{ \beta= \,\! }[/math] shape parameter (or slope)
[math]\displaystyle{ \gamma= \,\! }[/math] location parameter (or failure free life)